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Mirrors > Home > ILE Home > Th. List > elpr | Unicode version |
Description: A member of an unordered pair of classes is one or the other of them. Exercise 1 of [TakeutiZaring] p. 15. (Contributed by NM, 13-Sep-1995.) |
Ref | Expression |
---|---|
elpr.1 |
Ref | Expression |
---|---|
elpr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elpr.1 | . 2 | |
2 | elprg 3517 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wo 682 wceq 1316 wcel 1465 cvv 2660 cpr 3498 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-un 3045 df-sn 3503 df-pr 3504 |
This theorem is referenced by: prmg 3614 difprsnss 3628 preqr1 3665 preq12b 3667 prel12 3668 pwprss 3702 pwtpss 3703 unipr 3720 intpr 3773 zfpair2 4102 elop 4123 ordtri2or2exmidlem 4411 onsucelsucexmidlem 4414 en2lp 4439 reg3exmidlemwe 4463 xpsspw 4621 acexmidlem2 5739 2oconcl 6304 exmidpw 6770 renfdisj 7792 fzpr 9825 maxabslemval 10948 xrmaxiflemval 10987 isprm2 11725 bj-zfpair2 13035 ss1oel2o 13116 |
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